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To solve this problem, we will break it down step by step. The given data includes:

- Inductance \( L = 2.9 \, \text{H} \)
- Resistance \( R = 8.2 \, \Omega \)
- Battery voltage \( \epsilon = 100 \, \text{V} \)
- Time after connection \( t = 0.11 \, \text{s} \)

We are asked to find:
1. The rate at which energy is being stored in the magnetic field.
2. The rate at which thermal energy is appearing in the resistance.
3. The rate at which energy is being delivered by the battery.

### Step 1: Current in the circuit
For an RL circuit, the current \( I(t) \) as a function of time is given by:

\[
I(t) = \frac{\epsilon}{R} \left(1 - e^{-\frac{R}{L} t}\right)
\]

Substituting the values:

\[
I(0.11) = \frac{100}{8.2} \left(1 - e^{-\frac{8.2}{2.9} \cdot 0.11}\right)
\]

### Step 2: Energy stored in the magnetic field
The energy stored in the magnetic field in an inductor is:

\[
U_B = \frac{1}{2} L I^2(t)
\]

We can substitute the current \( I(0.11) \) found in Step 1 into this formula.

### Step 3: Thermal energy in the resistor
The power dissipated as thermal energy in the resistor is:

\[
P_R = I^2(t) R
\]

Again, substitute the current \( I(0.11) \).

### Step 4: Total power delivered by the battery
The total power delivered by the battery is given by:

\[
P_{\text{battery}} = \epsilon I(t)
\]

### Let's calculate the values.

I'll proceed with the necessary calculations now.Here are the calculated values:

1. **Current at \( t = 0.11 \) s**: \( I(0.11) = 3.26 \, \text{A} \)
2. **(a) Rate at which energy is being stored in the magnetic field**: \( U_B = 15.41 \, \text{J/s} \)
3. **(b) Rate at which thermal energy is appearing in the resistance**: \( P_R = 87.14 \, \text{J/s} \)
4. **(c) Rate at which energy is being delivered by the battery**: \( P_{\text{battery}} = 325.99 \, \text{J/s} \)

Would you like more details or have any questions? 

Here are some related questions to deepen your understanding:

1. How would the current change if the resistance were higher?
2. How is the energy stored in the magnetic field related to inductance and current?
3. How can we increase the rate at which thermal energy appears in the resistor?
4. How does the time constant \( \tau = L/R \) affect the circuit's response time?
5. What happens to the energy stored in the magnetic field after a long time?

**Tip:** In RL circuits, the time constant \( \tau = \frac{L}{R} \) controls how quickly the current reaches its steady state.

A coil with an inductance of 2.9 H and a resistance of 8.2 Ω is suddenly connected to an ideal battery with ε = 100 V. At 0.11 s after the connection is made, what is the rate at which (a) energy is being stored in the magnetic field, (b) thermal energy is appearing in the resistance, and (c) energy is being delivered by the battery?

Explore how energy is stored and dissipated in an RL circuit with a coil of 2.9 H inductance and 8.2 Ω resistance. This detailed solution covers exponential current growth, power dissipation, and battery energy delivery at 0.11 s after connection to a 100 V battery.

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